Introducing one-shot work into fluctuation relations
Abstract
Two approaches to small-scale and quantum thermodynamics are fluctuation relations and one-shot statistical mechanics. Fluctuation relations (such as Crooks' theorem and Jarzynski's equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches feature the same notions of work and the same notions of probability distributions over possible work values. The two approaches are alternative toolkits with which to analyze these distributions. To combine the toolkits, we show how one-shot work quantities can be defined and bounded in contexts governed by Crooks' theorem. These bounds provide a new bridge from one-shot theory to experiments originally designed for testing fluctuation theorems.
Additional Information
© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. RECEIVED 23 February 2015; REVISED 19 July 2015; ACCEPTED FOR PUBLICATION 10 August 2015; PUBLISHED 11 September 2015. The authors are grateful for conversations with Anna Alemany, Janet Anders, Cormac Browne, Tanapat Deesuwan, Alex Lucas, Jonathan Oppenheim, Felix Pollock, and Ibon Santiago. This work was supported by a Virginia Gilloon Fellowship, an IQIM Fellowship, support from NSF grant PHY-0803371, the FQXi Large Grant for 'Time and the Structure of Quantum Theory,' the EPSRC, the John Templeton Foundation, the Leverhulme Trust, the Oxford Martin School, the National Research Foundation (Singapore), and the Ministry of Education (Singapore). The Institute for Quantum Information and Matter (IQIM) is an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation. VV and OD acknowledge funding from the EU Collaborative Project TherMiQ (Grant Agreement 618074). NYH was visiting the University of Oxford under the auspices of Jonathan Barrett and the Department of Atomic and Laser Physics while much of this paper was developed.Attached Files
Published - Halpern_2015_New_J._Phys._17_095003.pdf
Submitted - 1409.3878v1.pdf
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Additional details
- Alternative title
- Unification of fluctuation theorems and one-shot statistical mechanics
- Eprint ID
- 50107
- Resolver ID
- CaltechAUTHORS:20140929-151759341
- Virginia Gilloon Fellowship
- Institute for Quantum Information and Matter (IQIM)
- NSF
- PHY-0803371
- Foundational Questions Institute (FQXI)
- Engineering and Physical Sciences Research Council (EPSRC)
- John Templeton Foundation
- Leverhulme Trust
- Oxford Univerisity
- National Research Foundation (Singapore)
- Ministry of Education (Singapore)
- Gordon and Betty Moore Foundation
- European Research Council (ERC)
- 618074
- Created
-
2014-09-29Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter